Question:

You have a 3-quart bucket, a 5-quart bucket, and an infinite supply of water. How can you measure out exactly 4 quarts?

.

.

C

A

P

T

A

I

N

I

N

T

E

R

V

I

E

W

.

.

There are a number of elegant ways to solve this puzzle. Most inter-viewers will favor the solution with the fewest number of steps.

Optimum Solution

1. Fill the 3-quart bucket and pour into the 5-quart bucket.
2. Again, fill the 3-quart bucket and pour into the 5-quart bucket to the brim. That leaves 1 quart remaining in the 3-quart bucket.
3. Empty the 5-quart bucket.
4. Pour the 1 quart into the 5-quart bucket.
5. Fill the 3-quart bucket again and add it to the 1 quart to make 4 quarts.

Alternative Solution

1. Fill the 5-quart bucket to the brim.
2. Pour the contents into the empty 3-quart bucket until it is full. Now there are 2 quarts in the 5-quart bucket.
3. Empty the 3-quart bucket.
4. Pour the 2 quarts from the 5-quart bucket into the 3-quart bucket.
5. Refill the 5-quart bucket.
6. Fill the 3-quart bucket with 1 quart, leaving 4 quarts in the 5-quart bucket.

Creative Solution

1. Fill 5-quart bucket and pour 3 quarts of water into 3-quart bucket, leaving 2 quarts in 5-quart bucket.
2. Refill the 5-quart bucket.
3. Carefully submerge the 3-quart bucket (now containing 2 quarts of water) into the 5-quart bucket to the brim of the smaller bucket. Now 3 quarts of water from the larger bucket are displaced. Now 2 quarts remain in the 5-quart bucket.
4. Remove the smaller bucket and transfer its 2 quarts into the 5-quart bucket with its 2 quarts.

Xi Ye, a student at the Illinois Mathematics and Science Academy in Aurora, Illinois, objects to the creative solution on the following grounds: “When you submerge the 3-quart bucket into the 5-quart bucket, the volume of the 3-quart bucket would count in the volume of the water displaced from the larger bucket,” he says. Xi Ye reminds us that unless the interviewer specifies a bucket without physical mass, creative solutions often bump up against reality.